远程协作实现高维量子态间的精确转换

Conclusive qudit states transformation implemented by remote parters

利用二维远程幺正旋转,Alice和Cindy远程协助Bob将他未知的d维初始量子态精确地转换为目标态.方案中,Alice和Cindy分别根据她们已知的初态和目标态的概率幅和相因子联合设计一理想的正定算符值测量(POVM),它作用于Bob的(2d?1)维直和空间.可用2(d?1)个二维远程幺正旋转实现该远程POVM.值得注意的是,仅需2(d?1)个二维Bell态(ebit)和3(d?1)个二维经典通信(cbit)就可精确地实现该远程态映射.给出了方案的成功概率.该方案可推广到初态和目标态的相因子信息分别被网络中N个不同端点的操控者共同掌握的情形.方案的简单性、精确性以及资源的有效利用等特点,使得其在目前的实验条件下更具可行性和更加适用于大规模量子网络.

Alice, Cindy, and Bob are three remote parties. We present a scheme which allows Alice and Cindy to transform probabilistically and conclusively Bob＇s unknown d-level quantum（qudit） state into another. In this scheme, the remote positive operator valued measurements（POVM） lies at the heart. Based on the knowledge of probability amplitudes and phase factors of Bob＇s original state and target state, Alice and Cindy could construct jointly the required optimal POVM, which acts remotely on Bob＇s（2d？1）-dimensional direct sum space. We construct a quantum network for realizing the remote POVM with 2（d？1） remote two-level unitary rotations, and thus provide a feasible physical means to realize the remote POVM. The fact that the remote POVM could be realized using only 2（d？1） two-level Bell states（ebits） and 3（d？1） two-level classical communications（cbits） is notable. This scheme can be generalized to implement conclusively the（N＋2）-party remote qudit state transformation via（d？1）（N＋1）-body two-level GHZ states, in which the phase factors of Bob＇s original state and target state are shared jointly by N agents. The success probability of implementing this remote state transformation is also investigated. This scheme is simpler but conclusive, and more efficient but with less resource, which will make it more feasible with the current experimental technology and more suitable for large-scale quantum network.